Difference Scheme For The Generalized Compound KdV-Burgers Equation

In this paper, the numerical methods for the initial-boundary problem of the generalized compound KdV-Burgers equation are investigated. The generalized compound KdV-Burgers equation which appears in a lot of physics model is one of important model equation in nonlinearity study of many science fields. The solitary waves solutions were broadly applied in quantized field theory, plasma physics and solid state physics.The generalized compound KdV-Burgers equation changes to equations with different physical significance corresponding to the fact that the parameter takes different values. At the same time, this equation includes the effects of the nonlinearity dispersive items and dissipative items, so it is very necessary and important to extensively study the generalized compound KdV-Burgers equation.In this paper, the main steps about solving the problems for determining solutions of partial differential equation by finite difference method have been introduced, several basic concepts such as truncation error, convergence, stability are stated, the Fourier series methods of analyzing the stability of difference scheme are studied, the expressions of difference coefficient operator are given.The difference scheme is constructed for the generalized compound KdV-Burgers equation by the method of Taylor series approximation. The finite-difference format of the existing literature are reasonably extended. The scheme depends on ten mesh points, it is linearized, implicit and two-level difference schemes which starts by itself.The local stability analysis is discussed by the priori estimates for numerical solution. The linearized implicit difference scheme for the generalized compound KdV-Burgers equation is absolutely stable. Numerical phase and phase error are analyzed in special case. Algorithm analysis and numerical examples are given. The numerical solution and the exact solution are compared. Numerical results for the generalized compound KdV-Burgers equation using the linearized implicit method are reported. Theoretical analysis and computational result are fitted each other. The approach of numerical imitates for solving nonlinearity equation is provided.